Question

In: Statistics and Probability

Most penguin species are not sexually dimorphic, which means they lack obvious outward body characteristics which...

Most penguin species are not sexually dimorphic, which means they lack obvious outward body characteristics which indicate sex. Observation of behavior or a blood test can determine Penguin sex. A penguin researcher is interested in estimating the proportion of females in a large penguin population. She takes a random sample of n = 20 penguins and determines the sex of each one using a blood test. She finds 12 males and 8 females. Let π be the proportion of females in the population.

(a) Find a point estimate of π.

(b) Find the estimated standard deviation of your estimate.

(c) Is it reasonable to compute a 95% confidence interval for π using the normal approximation in this case? If it is possible, explain why, and make the interval. If it is not reasonable, explain why.

(d) Are the data strong evidence the population proportion of females is different from 63%? Run a test at level α = .05 to find out.

Expert Solution

(a)

The point estimate of π is

(b)

The estimated standard deviation of your estimate is

(c)

Since number of successes and failures both are greater than 5 so normal approximation can be used.

(d)

Conclusion: The data provides strong evidence the population proportion of females is different from 63%.

orchestra answered 2 years ago

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